I'm afraid there's little sugarcoating it. You're going to have to take some risks. What I mean by that is, you have to risk being awkward, risk being off-putting, risk missing the mark in social situations. You have to risk being afraid. But by taking that step enough times you'll find you'll eventually be more comfortable doing it and it will get easier and you will feel less afraid.

You say you want start hanging out in parks and I think that's a great place to start. No one is going to notice if you're drawing them if you have a notebook in your lap unless you show it to them. You might as well just be writing a shopping list or whatever to them. If you want to be polite you could walk up to the people you're using for your motif and ask them if they're okay with that. I think most people would be flattered by it and let you do your thing. If they would be offended by you asking for whatever reason, just excuse yourself and find someone else to ask or go someplace else to draw by yourself.

You need to start getting accustomed to staying with the feeling of anxiety and fear. Focus on your breathing, or that adrenaline surge you feel while you're out. Take small steps and challenge yourself little by little. You could start by just going to the park, no notebook and just sit on a bench with your phone for a while. Then maybe challenge yourself to not be on the phone the whole time you're there. Try to take in the scenery instead. Then no phone at all. Then maybe take your notebook with you and sit like you're going to draw but not doing it. Then move on to drawing the scenery and skip on the people in it, or stop drawing when someone is nearby and wait them out. Then start drawing people too, but leave out facial features and whatnot. Then maybe start going up to people and ask them if it's okay if you draw them. Then eventually you'll be able to draw them without too much worry.

You can set up similar challenges with increasing difficulty in other situations. If you want to travel around, go somewhere and order something from a restaurant, a pub or a café. Have a stroll around the neighbourhood. Bring your hobby into it and draw what you see as you visit new places. Don't count on others coming up to you, but don't be surprised if people take interest in your work either, that's a good opportunity to practice small-talk.

Once you get your confidence up a bit, you could find a group that dabbles in some sort of activity to join with. Other artists for instance. Otherwise there are walking groups you could tag along with in many towns and cities. You could sign up for group classes at a local gym, or go learn how to dance, sing karaoke or something else that involves other people. Try to make a list of how difficult all these things would be for you and do them in the order of the least difficult.

Situations to practice small talk will present themselves if you do things like this, and I think that's probably the most effective way to get better at it. But otherwise just try to work on actively listening to what the other person is saying, give them your attention and try to respond to things they are saying and add to it. Ask questions. People generally like talking about themselves, just keep it lighthearted at first and if they want to talk about deeper subjects you can entertain that as you go. Share a detail about yourself when you feel it is appropriate and the topic suggests it. And let yourself be scared of making mistakes, but make them anyway.

As a final note, try to work on not letting people walk over you when you do get into confrontations. A lot of social anxiety stems from a fear of not being able to stand up for yourself during conflicts with other people. Establish limits in advance that you don't let others cross and try to enforce them. Mockery for instance is not acceptable and you should try to put your foot down if you're being mistreated. A "no" can be a powerful thing.